We extend the definition of analytic and Reidemeister torsion for closed compact iemannian manifolds, to compact Riemannian manifolds with boundary (M, δ M), given a parallel at bundle F of A-Hilbert modules of finite type and a decomposition of the boundary δM = -M ⊔ δ+M into disjoint components. When F is induced from the universal covering of M, and the fundamental group of M is infinite, these torsions are known as the L2-analytic resp. 2-Reidemeister torsions. If the system (M, δ-M, δ+M, F) is of determinant class we compute he quotient of the analytic and the Reidemeister torsion and prove gluing formulas for both of hem. In particular we answer positively Conjecture 7.6 in [LL]. If F is induced from a Γ-principal overing where Γ is a residually finite group, we derive from work of Lück, that the system (M, δ-M, δ+M, F) is of determinant class.

Burghelea, D; Friedlander, L; Kappeler, T (1999). *Torsions for manifolds with boundary and glueing formulas.* Mathematische Nachrichten, 208(1):31-91.

## Abstract

We extend the definition of analytic and Reidemeister torsion for closed compact iemannian manifolds, to compact Riemannian manifolds with boundary (M, δ M), given a parallel at bundle F of A-Hilbert modules of finite type and a decomposition of the boundary δM = -M ⊔ δ+M into disjoint components. When F is induced from the universal covering of M, and the fundamental group of M is infinite, these torsions are known as the L2-analytic resp. 2-Reidemeister torsions. If the system (M, δ-M, δ+M, F) is of determinant class we compute he quotient of the analytic and the Reidemeister torsion and prove gluing formulas for both of hem. In particular we answer positively Conjecture 7.6 in [LL]. If F is induced from a Γ-principal overing where Γ is a residually finite group, we derive from work of Lück, that the system (M, δ-M, δ+M, F) is of determinant class.

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Uncontrolled Keywords: | Torsions;manifolds with boundaries;glueing formulas |

Language: | English |

Date: | 1999 |

Deposited On: | 18 Feb 2010 13:06 |

Last Modified: | 05 Apr 2016 13:26 |

Publisher: | Wiley-Blackwell Publishing, Inc. |

ISSN: | 0025-584X |

Publisher DOI: | https://doi.org/10.1002/mana.3212080103 |

Related URLs: | http://www.ams.org/mathscinet-getitem?mr=1719799 |

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